Thermal evolution of the Schwinger model with Matrix Product Operators

TL;DR

This paper uses tensor network methods, specifically matrix product operators, to study the thermal properties of the Schwinger model, demonstrating accurate extrapolations and consistency with analytical results across various temperatures.

Contribution

It introduces tensor network techniques for thermal evolution in lattice gauge theories and validates their effectiveness on the Schwinger model with systematic error control.

Findings

Reliable extrapolations in bond dimension, step width, system size, and lattice spacing.

Consistent results with analytical predictions over a broad temperature range.

Effective capture of high-temperature behavior with small lattice spacings.

Abstract

We demonstrate the suitability of tensor network techniques for describing the thermal evolution of lattice gauge theories. As a benchmark case, we have studied the temperature dependence of the chiral condensate in the Schwinger model, using matrix product operators to approximate the thermal equilibrium states for finite system sizes with non-zero lattice spacings. We show how these techniques allow for reliable extrapolations in bond dimension, step width, system size and lattice spacing, and for a systematic estimation and control of all error sources involved in the calculation. The reached values of the lattice spacing are small enough to capture the most challenging region of high temperatures and the final results are consistent with the analytical prediction by Sachs and Wipf over a broad temperature range.